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Popular >

simplify ln((3e^4x^2)^2)

Solution

simplify

ln ((3 e^{4} x^{2})^{2})

Solution

2 (ln (3 x^{2}) + 4)

Solution steps

ln ((3 e^{4} x^{2})^{2})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 2 ln (3 e^{4} x^{2})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (3 e^{4} x^{2}) = ln (3 x^{2}) + ln (e^{4})

= 2 (ln (3 x^{2}) + ln (e^{4}))

Simplify

ln (e^{4}) : 4

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (3 x^{2}) = ln (3) + ln (x^{2})

= 2 (ln (x^{2}) + 4 + ln (3))

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 2 (2 ln (x) + 4 + ln (3))

ln (3) + 2 ln (x) + 4 = ln (3 x^{2}) + 4

= 2 (ln (3 x^{2}) + 4)

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Frequently Asked Questions (FAQ)

What is ln((3e^4x^2)^2) ?
The solution to ln((3e^4x^2)^2) is 2(ln(3x^2)+4)